Least Common Multiple (LCM) of 24 and 133
The least common multiple (LCM) of 24 and 133 is 3192.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 24 and 133?
First, calculate the GCD of 24 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 133 = 0 remainder 24 |
| 2 | 133 ÷ 24 = 5 remainder 13 |
| 3 | 24 ÷ 13 = 1 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 147 | 21462 |
| 105 and 122 | 12810 |
| 15 and 116 | 1740 |
| 79 and 188 | 14852 |
| 148 and 44 | 1628 |